hwB04 - ENEE 241 02* HOMEWORK ASSIGNMENT 4 Due Fri 02/08...

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ENEE 241 02* HOMEWORK ASSIGNMENT 4 Due Fri 02/08 Consider the discrete-time sinusoids x [ n ] = cos ± 3 πn 4 + 2 π 3 and y [ n ] = cos ± πn 5 + 2 π 3 (i) (4 pts.) What is the period N of x [ · ]? Use MATLAB to generate a discrete plot of the first four periods of x [ · ], (i.e., for n = 0 ,..., 4 N - 1.) (ii) (4 pts.) How many different sinusoids of the form cos( ωn ) are periodic with the same fundamental period as x [ · ]? Determine the values of ω in [0 , 2 π ) that produce these sinusoids. (iii) (4 pts.) The sequence v [ · ] is formed by taking every second sample in y [ · ], i.e., v [ n ] = y [2 n ] Write an equation for v [ n ]. What is the period of v [ · ]? (iv) (4 pts.) Use reasoning (possibly aided by MATLAB) to determine whether x [ n ] + y [ n ] is periodic. If it is, what is its fundamental period? (v) (4 pts.) Is the function z [ n ] = x [ n ] 2 periodic? If it is, what is its fundamental period? Solved Examples
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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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hwB04 - ENEE 241 02* HOMEWORK ASSIGNMENT 4 Due Fri 02/08...

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